Contents
Biography
Preface
Acronyms
1. Composite analysis overview 1
1.1. Introduction 1
1.1.1. History of composites 1
1.1.2. Applications of composites in aircrafts 3
1.2. Composite laminates 5
1.2.1. Definition and constituents 5
1.2.2. Plies 6
1.2.3. Laminates 7
1.3. Analysis schemes 9
1.3.1. Basic analysis schemes 9
1.3.2. Basic equations 11
1.3.3. Existing analysis theories 14
1.3.4. Challenges 16
1.3.5. Future developments 19
1.4. General Hooke’s law 20
1.4.1. Hyperelastic materials 20
1.4.2. Monoclinic materials 22
1.4.3. Orthotropic materials 22
1.4.4. Isotropic materials 24
1.4.5. Plane stress-reduced constitutive relations 24
1.4.6. Transformation of material coefficients 25
1.5. Energy principles 27
1.5.1. Virtual displacement principle 27
1.5.2. Hamilton’s principle 30
1.5.3. Mixed variational principles 31
References 33
2. Shear deformation theories 35
2.1. Introduction 35
2.2. Classical laminated plate theory 36
2.2.1. Displacement fields 36
2.2.2. Kinematic equation 38
2.2.3. Constitutive equations 42
2.2.4. Governing equations 45
2.3. First-order shear deformation theory 47
2.3.1. Displacement fields 47
2.3.2. Kinematic equation 48
2.3.3. Shear correction factors 50
2.3.4. Constitutive equations 50
2.3.5. Governing equations 52
2.4. High-order shear deformation theories 53
2.4.1. Second-order shear deformation theory 53
2.4.2. Third-order shear deformation theory 55
2.4.3. Higher-order shear deformation theories 58
2.5. Finite element formulations 58
2.5.1. CLPT 58
2.5.2. FSDT 63
2.5.3. TSDT 64
2.5.4. Numerical examples 68
References 70
3. State space theory 71
3.1. Introduction 71
3.2. Hamiltonian canonical equation of laminated plates 72
3.2.1. Hamiltonian canonical equation of individual layer 72
3.2.2. Exact solution of simply support single layer plates 74
3.2.3. Hamiltonian canonical equation of laminated plates 77
3.3. H-R variational principle of laminated plates 79
3.3.1. H-R variational principle in rectangular coordinate system 79
3.3.2. H-R variational principle in cylindrical coordinate system 84
3.3.3. Numerical examples 86
3.4. Finite element formulation of state space theory 87
3.4.1. Hamiltonian isoparametric element 87
3.4.2. Governing equations 90
3.4.3. Boundary conditions 91
3.4.4. Precise time-integration 92
3.4.5. Free vibration 93
3.4.6. Numerical examples 94
3.5. Meshfree formulation of state space theory 95
3.5.1. Interpolation using radial basis functions 95
3.5.2. Radial basis functions 98
3.5.3. Numerical examples 99
3.6. Bonding imperfection in composite laminates 101
3.6.1. Bonding imperfection 101
3.6.2. State space equation of bonding imperfection problems 102
3.6.3. Numerical examples 104
References 109
4. Layerwise theories 111
4.1. Introduction 111
4.2. Integrate layerwise methods 112
4.2.1. Generalized laminate plate theory 112
4.2.2. Layerwise FEM 113
4.2.3. Other ILWMs 113
4.3. Reddy’s layerwise theory 114
4.3.1. Displacement fields 114
4.3.2. Euler equations 116
4.3.3. Constitutive equations 120
4.3.4. Finite formulations 121
4.3.5. Numerical examples 122
4.4. Discrete layerwise theories 127
4.4.1. Development of DLWM 127
4.4.2. Displacement-based DLWM 128
4.4.3. Carrera’s unified formulation 132
4.4.4. Three-field variables DLWM 134
4.4.5. Multiparticle model of multilayered materials 135
References 136
5. Extended layerwisemethod 139
5.1. Introduction 139
5.2. Extended layerwise method of laminated plates 140
5.2.1. Displacements fields 140
5.2.2. Description of transverse crack 145
5.2.3. Hamilton’s principle and Euler–Lagrange equations 148
5.2.4. Constitutive equations 151
5.2.5. Finite element formulations 152
5.2.6. Time integrations 155
5.2.7. Numerical examples 156
5.3. Extended layerwise method of doubly-curved laminated shells 167
5.3.1. Geometric equations of laminated shells 167
5.3.2. Hamilton’s principle and Euler–Lagrange equations 170
5.3.3. Constitutive equations 173
5.3.4. Governing equations 176
5.3.5. Full extended layerwise method 179
5.3.6. Numerical examples 182
5.4. Fracture analysis of composite laminates 188
5.4.1. Equivalent domain integral method 188
5.4.2. Interaction integral method of isotropic materials 190
5.4.3. Interaction integral method of orthotropic materials 191
5.4.4. Interaction integral method of dynamic problems 192
5.4.5. Local remeshing scheme 193
5.4.6. Maximum circumferential tensile stress criterion 195
5.4.7. VCCT based on XLWM 196
5.4.8. Determination of delamination front 198
5.4.9. Numerical examples 201
5.5. Fast uniform-grid delamination scheme 208
5.5.1. The fast uniform-grid delamination scheme 208
5.5.2. Delamination re
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